A man has four ships A, B, C, and D. We know how these ships are. Each ship can

Question

A man has four ships A, B, C, and D. We know how these ships are. Each ship can either goes fast (f) or goes slowly (s) that day. An infotmation is a sequence of the four results about information of each ship A, B, C, and D, respectively. For instance, ffss is the information that the ships A and B can goes fast and ships C and D goes slowly that day. 1) What are the elements of the sample space of this story? 2) What are the elements of the CF(ship c goes fast) and BS(ship b goes slowly)?. 3) Are CF and BS mutually exclusive? 4) Are CF and BS collectively exhaustive? e) What are the elements of the Z(at least two ships can goes fast) and T(3 ships goes slowly)?5) Are Z and T mutually exclusive? or Z and T collectively exhaustive?

Explanation / Answer

1. Sample space S = {ssss, sssf, ssfs, ssff, sfss, sfsf, sffs, sfff, fsss, fssf, fsfs, fsff, ffss, ffsf, fffs, ffff}

2. CF = {ssfs, ssff, sffs, sfff, fsfs, fsff, fffs, ffff}

BS = {ssss, sssf, ssfs, ssff, fsss, fssf, fsfs, fsff}

CF and BS = {ssfs, ssff, fsfs, fsff}

3. Since CF and BS is not empty, the events are not mutually exclusive.

CF or BS = {ssss, sssf, ssfs, ssff, sffs, sfff, fsss, fssf, fsfs, fsff, fffs, ffff}

Since CF or BS does not contain all 16 elements of S, CF and BS are not collectively exclusive.

4. Z = {ssff, sfsf, sffs, sfff, fssf, fsfs, fsff, ffss, ffsf, fffs, ffff}

T = {sssf, ssfs, sfss, fsss}

Z and T = {}

5. Since Z and T is empty, the two events are mutually exclusive.

Z or T = {sssf, ssfs, ssff, sfss, sfsf, sffs, sfff, fsss, fssf, fsfs, fsff, ffss, ffsf, fffs, ffff}

Since Z or T does not contain one element (ssss) of S, Z and T are not collectively exhuastive.

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